Final answer:
The value of a is found by using the midpoint formula which gives M's x-coordinate as the average of Q's and R's x-coordinates. Solving the resulting equation, the value of a is determined to be -12.
Step-by-step explanation:
The question asks to find the value of the variable a such that the point Q(a, 4) will be one of the endpoints of a segment with midpoint M(-3, 7) and the other endpoint R(6, 10). To solve this, we make use of the midpoint formula for a line segment which states that the midpoint M has coordinates ((x1 + x2)/2, (y1 + y2)/2) where (x1, y1) and (x2, y2) are the coordinates of the endpoints. Since we know the coordinates of M and R, we can set up an equation to solve for a, which would be the x-coordinate of point Q:
- Midpoint M's x-coordinate: (-3) = (a + 6)/2
- Solving for a: -3 = (a + 6)/2 → -6 = a + 6 → a = -12
Therefore, the value of a is -12, and point Q has coordinates (-12, 4).